The term of Viesturs Burkāns, the current head of the anti-money laundering body, runs out in late May. He has been at the post since 1998.
This will be the first time the position is filled by way of a public tender.
"The anti-money laundering office ... needs radical change, which can be brought about with a transparent and clear selection process that would allow choosing the best manager for this institution important on the state level," said PM Māris Kučinskis.
The commission to choose the next head for the institution will be headed by State Chancellery director Jānis Citkovskis.
It will include representatives from the Finance Ministry, the Finance and Capital Market Commission (FKTK), the Constitution Protection Bureau, the Security Police and the Bank of Latvia.
Latvia's banking sector has come under scrutiny after ABLV Bank imploded following US accusations of money laundering.
Politicians have debated the introduction of a "shell company" tax that would discourage banks from serving high-risk clients. Meanwhile the Finance Ministry has suggested an audit of Latvia's finance authority, the FKTK, over its actions against ABLV Bank.